81.4.8 problem 5-9

Internal problem ID [21522]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 5. Integrating factors. Page 72.
Problem number : 5-9
Date solved : Thursday, October 02, 2025 at 07:46:44 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=2 y x -x \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

ode:=diff(y(x),x) = 2*x*y(x)-x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {1}{2}+{\mathrm e}^{x^{2}} c_1 \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 24

ode=D[y[x],x]==2*x*y[x]-x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2}+c_1 e^{x^2}\\ y(x)&\to \frac {1}{2} \end{align*}

✓ Sympy. Time used: 0.132 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*x*y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{x^{2}} \]